Episode 110: Mathhammer Part 1
In this episode, we talk about Mathhammer, which is using basic math to determine the offensive or defensive effectiveness of a particular unit in 40K. This is part 1 of a 2 part series. In part 1, we talk about the attack sequence and how to determine the probability of causing a wound. We then discuss the mechanics of the game that improve your odds, including re-rolls, modifiers, AP values, and volume of firepower. Finally we talk about variability and how randomness can impact your game plans.
Mathhammer is a way of determining the likelihood of causing a wound and figuring out the average number of wounds one unit can cause to another unit. Because 40K uses a D6 system with simple probabilities, you can figure out how likely a weapon or unit is in killing another pretty easily.
You can mathhammer out every unit if you like, but the real purpose of this podcast is to provide you with some guidelines to follow when list building and playing the game.
The D6 system
The probabilities for rolling a number or higher are the following:
- 2+: 83% (83.3%)
- 3+: 67% (66.6%)
- 4+: 50%
- 5+: 33% (33.3%)
- 6+: 17% (16.7%)
Every change on the dice required makes a big difference, so a +1 or -1 on these die rolls is important.
The Attack Sequence
Assuming you have at least one model in your unit in range and have line of sight (unless indirect fire), the formula is:
- Roll to hit: Ballistic skill/Weapon skill of firing unit
- Roll to wound
- Roll saves to get unsaved wounds. This is the probability of causing a wound.
- Roll damage
- Roll ignore wounds/Feel no Pain, to get the amount of wounds taken on average.
To improve your wounding efficiency, you can either:
- Shorten the attack sequence with auto-hit weapons or AP that ignores a save.
- Change the rolls at each step by attacking what you can reasonably hit/wound (go for the 4+).
- Use re-rolls and modifiers to improve your chances.
Rerolls and modifiers
Always maximize your re-rolls
Re-rolls to hit AND wound are actually even more impactful, because you are changing the probability of two separate rolls in the sequence to wound. You get more out of stacking hit AND wound re-rolls.
Modifiers to hit or wound are more impactful than a re-roll of 1, for example, which is why they are pretty scarce rules in the game.
Modifiers are best when you modify the roll that is worse. Both re-rolls and modifiers have a big impact on the units in this game, so always look for them in your codex to maximize your efficiency.
Volume of Attacks and Average Damage
A volume of attacks makes up for the sometimes poor probability of weapons to cause a wound. Especially if you need to hit or wound on 5s, you need a high volume to make up for the low probability.
Armor Penetration (AP) value
Always look for an AP value, at least -1, (a 2+ save is still good!), but -2 is a great “value” AP against many targets.
Random shots and random damage is hard to rely on and plan for. I’d rather have 2 than D3, or 3 versus D6, simply because it’s more consistent.
To improve your saving efficiency, you basically do the opposite of what you can do to increase efficiency. You can either:
- Lengthen the attack sequence with ignores wounding or FNP.
- Change the rolls at each step, a -1 to hit or wound.
- Improve the save with cover save or invuls
- Lessen the damage taken with -1 damage abilities
And of course, you can increase the “volume” of defense simply by having more models or wounds that your opponent has to remove.
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